Mr Castro made his announcement in his home town of San Antonio, Texas, where he was mayor from 2009 to 2014.

Aged 44 and long seen as a rising star in the party, he served as housing secretary under President Barack Obama and was on the list of Hillary Clinton's potential running mates for the 2016 election.

Having a Mexican grandmother, he has used his background to criticise Mr Trump's calls to build a wall to keep out migrants from Latin America.

Launching his bid under the slogan "One nation, one destiny", he said: "We say no to the construction of the wall and yes to the construction of communities."

He said his grandmother would have been amazed at his success and that of his brother Joaquin, a member of the US Congress.

"I've always believed that with big dreams and hard work, anything is possible in this country," he told the crowd.

Correspondents say Mr Castro does not have widespread name recognition and may struggle to make an impression in a crowded field.

Potential to build a following

It wasn't long ago that Julian Castro would have been considered a top-tier candidate for the Democratic presidential nomination. He was a well-regarded mayor of San Antonio, landed the keynote address at the 2012 Democratic National Convention and went on to a Cabinet position in the Obama administration.

Now, however, he may not even end up the most popular Texan in the race, if former congressman (and Democratic heartthrob) Beto O'Rourke decides to run. And there are other politicians - ones currently holding elective office or, like former Vice-President Joe Biden, with instant name recognition - who are generating more presidential buzz

Even if Mr Castro isn't quite the rising star he used to be - and, quite honestly, he has never been a particularly compelling public speaker - he still has the potential to build a following in the race to come. He's a third-generation Mexican-American at a time when Democrats are desperate to engage the growing Latino population in the US. He's young at a time when many Democrats are seeking generational change.

As a moderate in a party moving to the left, however, he's got his work cut out for him.

His launch comes a day after news emerged that Hawaii Congresswoman Ms Gabbard would also announce a bid.

In an interview due to air on CNN on Saturday evening, she says: "There are a lot of challenges that are facing the American people that I'm concerned about and that I want to help solve."

A native of American Samoa and an Iraq veteran, Ms Gabbard, 37, is seen as an outspoken figure on the left of the party.